How to remove this distinct line in my texture?
I'm not very good at texturing myself, but it's hard to tell what's wrong without seeing a picture of the unwrap.

That said, if there are texture lines in the middle of your object, you likely a) have a UV island or extra mesh face(s) in the middle of your table surface, or b) a non-tileable texture.

a) This could be because you've accidentally created an additional mesh face in the middle  of your table, or you've somehow double-mapped the texture to the face(s) in the middle. 
 - go to Edit mode (tab), then wireframe viewport mode (z), then Face select mode (3)
 -  one at a time, select each face around the discontinuity, them move them out of place (g) 
     - you should see the surrounding mesh stretch to the face location, Escape to cancel, go on to the next one
     - if you move a face out of place and there's still a face in the same place, you have a duplicated mesh. Escape to cancel
       - you can probably select all faces (a) and then go to Vertex > Remove Duplicates. Or just delete the excess vertices.  


if the mesh is fine, then there's an issue with your texture or unwrap


So, how big is the texture? 

If it is big enough to completely cover the unwrap island of the table surface without resizing, that's great. 
Otherwise, you MUST have a texture which is tileable or else you have to scale up the texture/scale down the UVs (same effect). 
I.e. a texture is tilieable if each side visually matches up with the opposite side - think wallpaper. (Again, can't tell what the texture is like without the unwrap view). 

If the texture is bigger than the unwrapped table meshes, you can shrink it down if you want, but not if it's smaller, without some loss in quality. Obviously better if the texture and islands are not resized at all. It's a bit difficult to tell how it will look without doing it.

If the texture is tileable or it's at least as big as the UVs then maybe you have duplicate UV faces attached to the same mesh face. I'm not sure if this is possible though. Try selecting each face in the 3d view and seeing what UVs are selected. There may be multiple UV faces that get highlighted if this is the case. But again, not sure if this is even possible.



The "line" looks to me to be a narrow strip of faces that is not attached contiguously to the surrounding mesh, i.e. the wrong texture is applied to the faces. It lines up with the table legs. I'm going to guess that you split the table top in line with the legs and extruded them from there. You probably accidentally created an extra strip and assigned the wrong texture.